Butterfly and Condor Spreads

I received a question recently about butterfly spreads. I never write about them, despite the fact that many individual investors like to trade such spreads.

Definition: An option strategy combining a bull and bear spread such that these two spreads share a common strike price. Frequently referred to as a 'fly.'

Example: The options in a butterfly are either all calls or all puts.

Buy AAPL Nov 100/110/120 call butterfly:

Buy 1 APPL Nov 100 call

Sell 2 AAPL Nov 110 calls

Buy 1 AAPL Nov 120 call

Note:

Long the 100/110 call spread; Short the 110/120 call spread

Buy AMZN Dec 105/110/115 put butterfly:

Buy 1 AMZN Dec 115 put

Sell 2 AMZN Dec 110 puts

Buy 1 AMZN Dec 105 put

Similarity to Condor spread:

The butterfly is a condor. The only difference is that there is a separation between the strike prices of the bull and bear spreads in the condor, and there is no separation (the spreads share one strike price) in the butterfly.

Condor Example:

Buy 10 SPY Jan 85 calls

Sell 10 SPY Jan 90 calls

Sell 10 SPY Jan 100 calls

Buy 10 Spy Jan 105 calls

In this condor, there is a 10-point separation.

Thus, the butterfly is similar to the condor. They are both members of the family of spreads called 'winged spreads.'

Iron Condor

The condor is equivalent to the iron condor. Why?

In the iron condor, instead of buying the bull call spread, the equivalent put spread is sold. Thus, the iron condor is:

Buy 10 SPY Jan 85 puts

Sell 10 SPY Jan 90 puts

Sell 10 SPY Jan 100 calls

Buy 10 Spy Jan 105 calls

Because selling the Jan 85/90 put spread is equivalent to buying the Jan 85/90 call spread, these two positions are equivalent.

Going one step further, the butterfly is equivalent to an iron condor in which there is zero separation between the strike prices of the bull and bear spread.

Bottom line: This is just another way of stating that iron condor traders can purchase a condor or butterfly and have a position that behaves similarly. The chosen strike prices represent the real differences in how the spreads perform in the real world.